A monster making some angry phone calls (7)
I believe the answer is:
gryphon
'a monster' is the definition.
(I know that gryphon is a type of mythical creature)
'some angry phone calls' is the wordplay.
'some' says the answer is hidden in the clue (some parts of the word are used).
'GRYPHON' is hidden in the letters of 'angry phone calls'.
'making' acts as a link.
(Other definitions for gryphon that I've seen before include "ordered to escort Alice" , "Eagle-headed, lion-bodied winged monster" , "Fabled beast, eagle-lion" , "Winged monster with lion body" , "Alice's mythic creature" .)